Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 137r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.75.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 138v); this page is its right half.
The machine reads it as
- simplice
- coefficientes terminorum in potentia polynomii sic definiuntur: sit
- polygonium X = a + b + C + drete Erit X = 4. + 4ab +6 a b + 12 a bc +24 abcd. in
- hac potentia, quae est quadru biquadratus ipsius X, sit terminus aebc, quaeritur ejus coefficiens 12
- Is est numerus omnium en tranum tabitatum traospositionum diseentium ipsius abe, velut it alac
- abc. a d. bac cab. bca. cba. abac. acab. abcadacba, baca. caba. Cum autem hic
- inoliri alibi docuimus, ut pro abe sit I2 t, = 12. pro a BC sit 1.2. 3. 45. 6. 2 - 5. 6. 7 = 210
- 1.2.
- 1.2. 3. 1.231.2
- loefficientes terminorum in potentia combinaoria bolynomii etiam definti possunt ex prioribus,
- modo sequenti. Voco autem poientiam combinutoriam velynomi cum aebibe xep
- non solum adhibentur X pro potistomio Va +b+C ret C. sed et y pro binionibis omnibus ab tac +bet et
- et Z pro ternionibus omnibus vabet abda acd + bed + ek. e BB pro sxternionibus omnibus, et ita
- porro. Eiit atb+c+det vel a = X et qu ∞XX- 2y vel xx = aa + 29, et
- a = X - 3Xy + 3Z. Et ita porri. ute ritu numerus coefficiens ipsius XyZ, (ex. gr.)
- in ab vel X.. Fiet ut 3 numeus dimensionum apparentum ipsus X9Z a 6 nundrum occultarum
- q(nim x habet 1, y habet 2, Zhabot 3, quia Y intet ab inti vabet abC) ut 6 mimeris
- permatabilitatum apparentium ipsius XyZ, (seu coefficiens ipsius abc in potentia polymmmii
- X9Z est 1. 23 6 = 1
- simplice) at quaesitum 12. e Itaque coeficient iimar eb pus dimenti a
- signum in potentia smiplice est semper + 1. in potentia combinatoria e positu simpade t ter pus dimendi daa
- XK = aa F2ab X = a + 3a b +6abc X= a +44b +6ab + 12 abc + 24 abcd
- ains diberum. Prenius Gnia p a edi dinaeniim t
- X= a +5ab+10ab+ +30 a bc +6 abcd + 120 abcde
- X = a +64b+15 ab130ab ab,60abc +120abcd + 9 abC,
- 1c
- 10a
- Brevint qad figuum forma qua abique d di tstimersidou apparex ts diff
- a = X
- p 91s 6250b 12 2000
- =X- 25973Z. 1.
- X=X- EKyt AX Z+ X(- 5XB. 5 y215)
- asqrent
- =X 4Xy+ 4X22y 242
- -X - 6Xy + B XZ +9X ( - 6XB, 6 X - 27 4 6y B13
- si a, b,c, et suit 1, fit, X = 12 3 456 y = D, 1, 3, 619,15 20, 0, 1, 4, 10 209 ( = 0,0pe, 1, 5,15 P= 0,0, 0, 0 110 ad vi
- si ergo rudices aequationis ponantur esse Data invatioore somme curu omres
- +qu YX.3 + etc. Ponendo radices es , suEt
- esse a; vel o pont C, etc. prit a = B et g a ab = et abC = Y; L habust
- ex
- X +eXC
- et erit aa = lp - 29 et = p - 3p9+ 3Y et a = p - 4 ppq. + 4pY + 29)-
- porri a = p3 - Sp9+SppYF5p99- Spes - 5qY + 5F. Et ita porro
- jerine
- , sed ita et ponafattentum adesses
- 10
- a, to e di
- noinvestidaletiat
- ntis jam et
- Assuno jam instar hypotheseos, quor raclix quaesita aequationis X, sit pelyno-
- 1s
- m P1 4, C, ∞5, B
- mium, seu X = le ex quae Lm, etc sunt quantitates itrationales, posito
- oeus cuique est aepartu
- sen reliagtnone sato
- porro Turpono easdem vel earum potentias conitinationessue quaslunque non dare ali
- quid rationale, em, lina, Um, et nisi forte eo cisu quo omnes simul ducuntur in
- se invicem. Si itaque nulla talis forma ex ipsis (exc epta forte illa unica) dat aliqid rationale.
- aqurgens
- lrcditd
- elic _ 129.3
- 1.2. 351
- 120. 6 - 0
- rimm (parium) habit X = a
- idem signum cum
- 38a
- 3125
- sese
- q
- 67
- 6250
- ane
- 68)
- t
- 628
- 3125
- D
- unt
Cite
Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 137r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0273?run=74